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Total Surface Area of Truncated Rhombohedron given Circumsphere Radius Formula

GoTotal Surface Area of Truncated Rhombohedron given Rhombohedral Edge Length Formula

GoTotal Surface Area of Truncated Rhombohedron Formula

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Total Surface Area of Truncated Rhombohedron is the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron. Check FAQs

TSA = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{4 \cdot r c}{\sqrt{14 - (2 \cdot \sqrt{5})}})}^{2})

TSA - Total Surface Area of Truncated Rhombohedron?r_c - Circumsphere Radius of Truncated Rhombohedron?

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius Example

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Here is how the Total Surface Area of Truncated Rhombohedron given Circumsphere Radius equation looks like with Values.

Here is how the Total Surface Area of Truncated Rhombohedron given Circumsphere Radius equation looks like with Units.

Here is how the Total Surface Area of Truncated Rhombohedron given Circumsphere Radius equation looks like.

3408.0547 = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{4 \cdot 20}{\sqrt{14 - (2 \cdot \sqrt{5})}})}^{2})

3408.0547m² = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{4 \cdot 20m}{\sqrt{14 - (2 \cdot \sqrt{5})}})}^{2})

3408.0547 = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{4 \cdot 20}{\sqrt{14 - (2 \cdot \sqrt{5})}})}^{2})

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Total Surface Area of Truncated Rhombohedron given Circumsphere Radius Solution

Follow our step by step solution on how to calculate Total Surface Area of Truncated Rhombohedron given Circumsphere Radius?

FIRST Step Consider the formula

TSA = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{4 \cdot r c}{\sqrt{14 - (2 \cdot \sqrt{5})}})}^{2})

Next Step Substitute values of Variables

∴

TSA = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{4 \cdot 20m}{\sqrt{14 - (2 \cdot \sqrt{5})}})}^{2})

Next Step Prepare to Evaluate

∴

TSA = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{4 \cdot 20}{\sqrt{14 - (2 \cdot \sqrt{5})}})}^{2})

Next Step Evaluate

∴

TSA = 3408.05466040375m²

LAST Step Rounding Answer

∴

TSA = 3408.0547m²

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius Formula Elements

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Functions

Total Surface Area of Truncated Rhombohedron

Total Surface Area of Truncated Rhombohedron is the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Truncated Rhombohedron

Circumsphere Radius of Truncated Rhombohedron

Circumsphere Radius of Truncated Rhombohedron is the radius of the sphere that contains the Truncated Rhombohedron in such a way that all the vertices are lying on the sphere.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumsphere Radius of Truncated Rhombohedron

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Total Surface Area of Truncated Rhombohedron

Go Total Surface Area of Truncated Rhombohedron given Rhombohedral Edge Length

TSA = \frac{({l e(Rhombohedron)}^{2}) \cdot ((3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15}))}{2}

Go Total Surface Area of Truncated Rhombohedron

TSA = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{2 \cdot l e}{3 - \sqrt{5}})}^{2})

Go Total Surface Area of Truncated Rhombohedron given Triangular Edge Length

TSA = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot ({(\frac{l e(Triangle)}{\sqrt{5 - (2 \cdot \sqrt{5})}})}^{2})

Go Total Surface Area of Truncated Rhombohedron given Area of Pentagon

TSA = (\frac{(3 \cdot (\sqrt{5 + (2 \cdot \sqrt{5})})) + (5 \cdot \sqrt{3}) - (2 \cdot \sqrt{15})}{2}) \cdot (4 \cdot \frac{A Pentagon}{\sqrt{5 + (2 \cdot \sqrt{5})}})

How to Evaluate Total Surface Area of Truncated Rhombohedron given Circumsphere Radius?

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius evaluator uses Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2) to evaluate the Total Surface Area of Truncated Rhombohedron, Total Surface Area of Truncated Rhombohedron given Circumsphere Radius formula is defined as the total quantity of plane enclosed by the entire surface of the Truncated Rhombohedron, calculated using its circumsphere radius. Total Surface Area of Truncated Rhombohedron is denoted by TSA symbol.

How to evaluate Total Surface Area of Truncated Rhombohedron given Circumsphere Radius using this online evaluator? To use this online evaluator for Total Surface Area of Truncated Rhombohedron given Circumsphere Radius, enter Circumsphere Radius of Truncated Rhombohedron (r_c) and hit the calculate button.

FAQs on Total Surface Area of Truncated Rhombohedron given Circumsphere Radius

What is the formula to find Total Surface Area of Truncated Rhombohedron given Circumsphere Radius?

The formula of Total Surface Area of Truncated Rhombohedron given Circumsphere Radius is expressed as Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2). Here is an example- 3408.055 = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*20)/(sqrt(14-(2*sqrt(5)))))^2).

How to calculate Total Surface Area of Truncated Rhombohedron given Circumsphere Radius?

With Circumsphere Radius of Truncated Rhombohedron (r_c) we can find Total Surface Area of Truncated Rhombohedron given Circumsphere Radius using the formula - Total Surface Area of Truncated Rhombohedron = (((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((4*Circumsphere Radius of Truncated Rhombohedron)/(sqrt(14-(2*sqrt(5)))))^2). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Truncated Rhombohedron?

Here are the different ways to Calculate Total Surface Area of Truncated Rhombohedron-

Total Surface Area of Truncated Rhombohedron=((Rhombohedral Edge Length of Truncated Rhombohedron^2)*((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15))))/2
Total Surface Area of Truncated Rhombohedron=(((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*(((2*Edge Length of Truncated Rhombohedron)/(3-sqrt(5)))^2)
Total Surface Area of Truncated Rhombohedron=(((3*(sqrt(5+(2*sqrt(5)))))+(5*sqrt(3))-(2*sqrt(15)))/2)*((Triangular Edge Length of Truncated Rhombohedron/(sqrt(5-(2*sqrt(5)))))^2)

Can the Total Surface Area of Truncated Rhombohedron given Circumsphere Radius be negative?

No, the Total Surface Area of Truncated Rhombohedron given Circumsphere Radius, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Truncated Rhombohedron given Circumsphere Radius?

Total Surface Area of Truncated Rhombohedron given Circumsphere Radius is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Truncated Rhombohedron given Circumsphere Radius can be measured.

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